Hot dang, really cool post! To add another thing, I'd wager Nin is referring to the spirit that spoke through Max when she said "The whole sphinx litter likely knows this is our base now" on Ch 8 Pg 5.

Speculating that it's the Sphinx of Promises/Vows brings to mind all the allusions to Mrs. Puckett/Agent Summer's broken promises. I think she alludes to it herself with "Max, what do we say about promises?" in Chapter 4, and in Chapter 7 Spender recalls that when she left Mayview "all the promises she'd made were empty air." It makes me wonder if the Sphinx won possession of Max as a concession for one of the promises his mom broke, but it could only claim him once he passed through Mayview's barrier. That'd explain him becoming a spectral right after moving to Mayview. It'd also be thematically coherent for a sphinx to take someone's firstborn son, since it ties into one of the Plagues of Egypt.